Problem: Bob the Wizard makes magical brooms. He charges $125$ gold pieces for each magical broom he makes for his customers. He also charges a one-time fee of $50$ gold pieces for his initial consultation. The total number $G$ of gold pieces Bob charges is a function of $x$, the number of magical brooms he makes. Write the function's formula. $G=$
The number of gold pieces Bob charges for each magical broom is constant, so we're dealing with a linear relationship. We could write the desired formula in slope-intercept form: $G= mx+ b$. In this form, $ m$ gives us the slope of the graph of the function and $ b$ gives us the $y$ -intercept. Our goal is to find the values of $ m$ and $ b$ and substitute them into this formula. We know that Bob charges $125$ gold pieces for each magical broom he makes, so the slope $ m$ is ${125}$, and our function looks like $G={125}x+ b$. We also know that Bob's initial fee is $50$ gold pieces, so the $y$ -intercept ${b}$ is ${50}$. Since ${m}={125}$ and ${b}={50}$, the desired formula is: $G={125}x+{50}$